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The Product of Automorphic Weighted Composition Operators on Hardy Space H <sup>2</sup>
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Abstract<p>Let <inline-formula> <tex-math><?CDATA $n\in {\mathbb{N}},{p}_{i}\in {\rm{U}},{\alpha }_{{P}_{i}}(z)=\frac{{p}_{i}-z}{1-{\bar{p}}_{i}z}(z\in {\rm{U}})$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mi>n</mi> <mo>∈</mo> <mi>ℕ</mi> <mo>,</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>∈</mo> <mi mathvariant="normal">U</mi> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> </mrow> </msub> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>−</mo> <mi>z</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <msub> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mi>i</mi> </msub> <mi>z</mi> </mrow> </mfrac> <mo stretchy="false">(</mo> <mi>z</mi> <mo>∈</mo> <mi mathvariant="normal">U</mi> <mo stretchy="false">)</mo> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula>, and let <inline-formula> <tex-math><?CDATA ${f}_{1}\in {H}^{\infty },i=1,\ldots,n$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>∈</mo> <msup> <mi>H</mi> <mi>∞</mi> </msup> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula>. We discuss the relation between the points <italic>p<sub>i</sub> </italic> in U and the functions <italic>f<sub>i</sub> </italic> in U and the properties of the product of automorphic weighted composition operators <inline-formula> <tex-math><?CDATA ${W}_{{f}_{1},{\alpha }_{{p}_{1}}}\,{W}_{{f}_{2},{\alpha }_{{p}_{2}}}\ldots {W}_{{f}_{i},{\alpha }_{pi}}$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> </msub> <mspace width="0.25em"></mspace> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>…</mo> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn3.gif" xlink:type="simple"></inline-graphic> </inline-formula> on Hardy space H<sup>2</sup>. In fact, it is very nice connection between analytic function theory and operator theory. In this paper, we give the sufficient and necessary conditions to be normal, unitary, hermitian operator on <italic>H</italic> <sup>2</sup> and we shall present the shape of the numerical range of it.</p>
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Wed Mar 14 2007
Journal Name
Journal Of Education College Wasit University
On the deviation of literary language
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DBN Rashid, Journal of Education College Wasit University 1(1):412-423, 2007

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Publication Date
Thu Feb 11 2021
Journal Name
Journal Of Legal Sciences
The Effects of The Pharmaceutical Discovery Process on The Researcher
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The process of discovering pharmaceuticals is of great importance in our contemporary life, in a way that without life becomes almost impossible, as this process is the first building block in the field of pharmaceutical industries to search for new methods and means of treatment and treatment. But in fact, the fact that talking about this process is not that simple and easy, because this process is complicated and difficult in a way that makes it take a time range that in some cases reaches what is permissible ten years to reach a chemical formula that can be used later in the manufacturing process Pharmacokinetics, and during this long period of time, this process will have a set of effects, some of which are specific to the researcher di

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Publication Date
Wed Jun 01 2022
Journal Name
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Hydrogenation of pyridine and hydrogenolysis of piperidine over <i>γ-</i>Mo<sub>2</sub>N catalyst: a DFT study
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Increasing demands on producing environmentally friendly products are becoming a driving force for designing highly active catalysts. Thus, surfaces that efficiently catalyse the nitrogen reduction reactions are greatly sought in moderating air-pollutant emissions. This contribution aims to computationally investigate the hydrodenitrogenation (HDN) networks of pyridine over the γ-Mo2N(111) surface using a density functional theory (DFT) approach. Various adsorption configurations have been considered for the molecularly adsorbed pyridine. Findings indicate that pyridine can be adsorbed via side-on and end-on modes in six geometries in which one adsorption site is revealed to have the lowest adsorption energy (

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Publication Date
Fri Jan 01 2010
Journal Name
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Synthesis and ldentification of metal complexes of 1- phenyl -3, (2'(S'phenyl amine)'l, 3, 4-thiad iazole'Z'yl) phenyl thiourea.
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Complexes of 1-phenyl-3-(2(-5-(phenyl amino)-1,3,4- thiadiazole-2-yl)phenyl) thiourea have been prepared and characteized by elemental analysis, Ff-[R, and u.v./ visible spectra moreover, determination of metal content M%o by flame atomic absorption spectroscopy, molar conductance in DMSO solution and magnetic moments (peffl. The result showed that the ligand (L) was coordinated to Mn*2, Ni*2, Ct*2,2n*2,Cd*2, and Hg*2 ions through the nitrogen atoms and sulpher atoms. From the result obtained, rhe following general formula [MLClz] has been given for the prepared complexes with an octahedral geometry around the metal ions for all complexes. where M= Mn*2, Ni*2, cu*2, zn*z, cd*z, and Hg*2 l= l-phenyl-3-(2-(5-(phenyl amino)-1, 3,

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Publication Date
Sat Feb 02 2019
Journal Name
Journal Of The College Of Education For Women
The Effect of Arab Environment on the Artist's Works August Renoir: The Effect of Arab Environment on the Artist's Works August Renoir
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Abstract:
This study is considerated one of many Studies above the standing of
the Islamic Arab nation which was chosen by God from other nations all over
the world . Some of these nations used to come to the Arab nation to take
whatever useful for them from the beginning of history till now . The
researcher deals in this study with a French artist who is well-know as
August Renoir . He traveled to Algeria and lived there . He was
influenced by the Islamic culture.
The study include. from chapter . chapter one deals with the framework of
programming (out line ) . Chapter two deals with the theoretical framework .
It includes five sections. Deals with the Islamic drawings(Arabesque) . section
three deals w

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Publication Date
Tue Oct 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
The Impact Of Means Of Support On The Intention Entrepreneurial Field Research On A Sample Of Algerian Students
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     The aim of this paper to study the effect of the implicit factors on the entrepreneurial spirit of the students of the Algerian university. Our structural model was proposed based on the model (Shapiro et Sokol, 1982) and the model (Ajzen, 1991). We tested it on a sample of 163 university students at the University of Algiers 3. The model consists of a set of variables (the intention of contracting as a dependent variable, structural and social educational support as independent variables). The results showed that educational and social support factors affect the entrepreneurial spirit of students more than structural support. The Applied Impacts are the enhancing of knowledge capacities of university stu

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The primary aim of the present study was to prepare a set of exercises on the multi-resistor VertiMax device and to identify the effect of these exercises on the development of the endurance of discus throwers under 16 years old. The design of the present study was experimental. Participants were selected using purposive sampling method. A total of 5 discuss players constituted the sample of the study. The authors found a significant improvement in the levels of endurance and performance as a result of the training on the VertiMax device. Therefore, it is recommendable to use exercises on the VertiMax device to improve the endurance and performance of under 16-years of age discus throwers.

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The Reliance of the Public of Baghdad on News Broadcasts on Satellite Channels as a Source of Information
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The importance of news broadcasts in society has increased after the domination of television over the mass media, especially after emerging the satellite channels, and spreading the satellite dishes among the public at large.

As well as the great role played by the modern technology in the transmission of news and events happening at once. Such role has contributed, significantly, in changing the concept and values ​​of the news. The live broadcast of the events filmed is the news itself.

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Mon Jan 01 2024
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